Virgin,
I believe the Atkins diet works because the usual inadvertant high protien diet. Researchers found that protien makes you less hungry calorie for calorie. So the truth of the matter seems to be eat more lean meat like chicken and fish (not fried).
If you want to take to much more reliable exercise method then it is important to do two things:
1) Eat more complex carb like pasta, honey, bananas, potato and greatly reduce simple carbs like sugar, snickers, etc!! Complex carbs do not provide an insulin rush, they are broken down gradually like the body of hours rather then the minutes (quick hit) of simple sugars.
2) When it comes to exercising don't fall into the trap of thinking that pain = gain. All pain = is injury, colds, flu and general tiredness. Exercising to loose weight means regular moderate exercise. It is very easy to run too fast when jogging. Generically speaking, it is something like the 65% of your max heart rate is the optimum fat buring zone. You burn less calories than 75-80% of max but you burn them from the right place. If you execise more vigourously then you just clear out your glycogen stores which means, when you eat they get topped up and the fat situation remains the same.
A bit simplistic, but you get the picture I hope.